Architecture induced by distributed backstepping design

An important problem in the distributed control of large-scale and infinite dimensional systems is related to the choice of the appropriate controller architecture. We utilize backstepping as a tool for distributed control of nonlinear infinite dimensional systems on lattices, and provide the answer to the following question: what is the worst case controller architecture induced by distributed backstepping design? We demonstrate that distributed backstepping design yields controllers that are intrinsically decentralized, with a strong similarity between plant and controller architectures. In particular, we study the ´worst case´ control design in which all interactions are cancelled at each step of backstepping. Any other backstepping strategy yields controllers with better information transmission properties. For this ´worst case´ situation we quantify the number of control induced interactions necessary to guarantee desired dynamical behavior of the infinite dimensional system. We also provide an example of systems on lattices and show how the controllers with favorable architectures can be designed.